Uncertainty is central to reliable inference

Simulation Study Visualizations

Authors

Affiliations

Björn S. Siepe

University of Marburg

Matthias Kloft

University of Marburg

Fridtjof Petersen

University of Groningen

Yong Zhang

University of Groningen

Laura F. Bringmann

University of Groningen

Daniel W. Heck

University of Marburg

1 Background

This document contains code to reproduce the visualizations of the simulation study in the manuscript. It also contains additional results not shown in the main manuscript.

2 Preparation

Load relevant packages:

library(tidyverse)
library(SimDesign)
library(here)
library(cowplot)
library(ggh4x)
library(pander)
library(MetBrewer)
source(here::here("scripts", "00_functions.R"))

Load the simulation results:

sim_results <- readRDS(here("output", "sim_results.RDS"))

# Create a cut version of the simulation results without MCMC diagnostics
sim_res_cut <- sim_results |>
  select(-contains("rhat")) |>
  select(-contains("divtrans"))

2.1 Data Wrangling

Prepare dataframe for visualization by giving proper names, removing unnecessary columns, and pivoting longer:

sr_edit <- sim_res_cut |> 
  mutate(
    dgp = factor(n_tp, levels = c(60, 120)),
    n_id = factor(n_id, levels = c(75, 200))
    ) |>
  # remove "reg_" from all column names
  rename_with(~str_remove(., "reg_")) |> 
  # remove everything before a "." in the column names
  rename_with(~str_remove(., ".*\\.")) |> 
  dplyr::select(-c("REPLICATIONS", "SIM_TIME", "SEED", "COMPLETED", "WARNINGS", "RAM_USED")) |>
  dplyr::select(-c("heterogeneity")) |> 
  # pivot longer except conditions cols
  pivot_longer(cols = -c("dgp", "n_tp", "n_id"), 
               names_to = "measure", 
               values_to = "value") |> 
  mutate(measure = str_replace(measure, "power_reg", "powerreg"),
         measure = str_replace(measure, "powertwoside_reg", "powertwosidereg"),
         measure = str_replace(measure, "poweroneside_reg", "poweronesidereg"),
         measure = str_replace(measure, "rmse_reg", "rmsereg"),
         measure = str_replace(measure, "bias_reg", "biasreg"),
         measure = str_replace(measure, "mse_reg", "msereg")) |>
  filter(!measure %in% c("strength_sd", "outstrength_sd", "instrength_sd")) |> 
  separate_wider_delim(measure, 
                       delim = "_",
                       names = c("pm", "outcome", "method", "summary")) |> 
  mutate(method = case_when(
    method == "gvar" ~ "GVAR",
    method == "gimme" ~ "GIMME",
    method == "mlvar" ~ "mlVAR",
    method == "bmlvar" ~ "BmlVAR"
  )) |>
  # treat method as factor and order 
  mutate(method = factor(method, levels = c("GVAR", "GIMME", "mlVAR", "BmlVAR"))) |>
  mutate(outcome = case_when(
    outcome == "beta" ~ "Temporal",
    outcome == "pcor" ~ "Contemporaneous",
    .default = outcome
  )) |>
  group_by(dgp, n_tp, n_id, pm, outcome, method) |>
  pivot_wider(names_from = summary, values_from = value) |> 
  ungroup()

Prepare different colors and settings for visualization:

meth_colors <- set_names(MetBrewer::met.brewer("Johnson")[c(1,2,4,5)],
                         c("GVAR", "mlVAR", "GIMME", "BmlVAR"))

3 Check Warnings and Errors

3.1 Errors

Check if any errors that led to non-convergence occurred:

# load results before resummarization, which contain potential error messages
sim_full_pre_resum <- readRDS(here("output", "sim_full.rds"))

sim_errors <- SimExtract(sim_full_pre_resum, "errors")

There were 0 error messages.

3.2 Warnings

We extract all warnings and rename them properly:

sim_warnings <- SimExtract(sim_full_pre_resum, what = "warnings")

sim_warnings |> 
  select(!c(heterogeneity, strength_sd, outstrength_sd, instrength_sd)) |> 
  rename("Deprecated dplyr function" = "WARNING:  c(\"Warning in NULL : `funs()` was deprecated in dplyr 0.8.0.\", \"Warning in NULL : Please use a list of either functions or lambdas: \\n\\n  # Simple nam",
         "Bulk ESSlow" = "WARNING:  Warning in NULL : Bulk Effective Samples Size (ESS) is too low, indicating posterior means and medians may be unreliable.\nRunning the chains for more i",
         "Potential Stan sampling problems" = "WARNING:  Warning in NULL : Examine the pairs() plot to diagnose sampling problems\n",
         "Tail ESS low" = "WARNING:  Warning in NULL : Tail Effective Samples Size (ESS) is too low, indicating posterior variances and tail quantiles may be unreliable.\nRunning the chains",
         "NA R-hat" = "WARNING:  Warning in NULL : The largest R-hat is NA, indicating chains have not mixed.\nRunning the chains for more iterations may help. See\nhttps://mc-stan.org/mi",
         "Divergent transition" = "WARNING:  Warning in NULL : There were 1 divergent transitions after warmup. See\nhttps://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup\nto find",
         "Exceeded maximum treedepth" = "WARNING:  Warning in NULL : There were 497 transitions after warmup that exceeded the maximum treedepth. Increase max_treedepth above 10. See\nhttps://mc-stan.org",
         "Rothman algorithm warning" = "WARNING:  Warning in Rothmana(data_l, data_c, lambdas$beta[i], lambdas$kappa[i], regularize_mat_beta = regularize_mat_beta,     regularize_mat_kappa = regulariz",
         "Variable naming warning" = "WARNING:  Warning in validityMethod(object) : The following variables have undefined values:  reg_intercept_z[1],The following variables have undefined values: ") |> 
  knitr::kable()

dgp	n_id	n_tp	Deprecated dplyr function	Bulk ESSlow	Potential Stan sampling problems	Tail ESS low	NA R-hat	Divergent transition	Exceeded maximum treedepth	Rothman algorithm warning	Variable naming warning
sparse	75	60	60	200	100	200	28	100	3	4759	35
sparse	200	60	0	200	1	199	15	1	0	12834	23
sparse	75	120	0	199	26	197	5	26	0	4555	2
sparse	200	120	0	200	0	163	3	0	0	12042	32

Unfortunately, we removed warnings from mlVAR during our simulation. However, in our additional simulations in 06_additional_mlvar_simulation.qmd, we noticed that warning messages from mlVAR were only related to the renaming of certain variables, so we assume that we did not miss any substantial warnings.

4 Point Estimates

Plot point estimate recovery (RMSE), helpful to understand the overall performance of the different methods.

plot_mse <- sr_edit |> 
  mutate(mcse = ifelse(is.na(mcse), 0, mcse)) |>
  mutate(outcome = factor(outcome, levels = c("Temporal", "Contemporaneous"))) |>
  filter(pm == "mse") |> 
  ggplot(aes(x = method, 
             y = mean, 
             colour = method
             )) +
  # add vertical line between methods
  geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
  geom_errorbar(aes(ymin = mean - 1*mcse,
                            ymax = mean + 1*mcse),
                        width = .8,
                 position = position_dodge(0.7),
                 show.legend = FALSE)+
  geom_point(position = position_dodge(0.7), 
             size = 1.2) +
  ggh4x::facet_nested(n_id ~ outcome + n_tp,
                      axes = "all",
                      remove_labels = "y") +
  scale_x_discrete(guide = guide_axis(angle = 90))+
  scale_y_continuous(expand = c(0, 0), limits = c(0,0.03)) +
  scale_color_manual(values = meth_colors) +
  theme_centrality() +
  theme(legend.position = "none",
        text = element_text(size = 22))+
  labs(title = "",
       x = "Method",
       colour = "Method",
       y = "MSE of Network Estimation")

plot_mse

Plot Bias:

plot_bias <- sr_edit |> 
  mutate(mcse = ifelse(is.na(mcse), 0, mcse)) |>
  mutate(outcome = factor(outcome, levels = c("Temporal", "Contemporaneous"))) |>
  filter(pm == "bias") |> 
  ggplot(aes(x = method, 
             y = mean, 
             colour = method
             )) +
  # add vertical line between methods
  geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
  geom_errorbar(aes(ymin = mean - 1*mcse,
                            ymax = mean + 1*mcse),
                        width = .8,
                 position = position_dodge(0.7),
                 show.legend = FALSE)+
  geom_point(position = position_dodge(0.7), 
             size = 1.2) +
  ggh4x::facet_nested(n_id ~ outcome + n_tp,
                      axes = "all",
                      remove_labels = "y") +
  scale_x_discrete(guide = guide_axis(angle = 90))+
  scale_y_continuous(expand = c(0, 0), limits = c(-0.1,0.1)) +
  scale_color_manual(values = meth_colors) +
  theme_centrality() +
  theme(legend.position = "none",
        text = element_text(size = 22))+
  labs(title = "",
       x = "Method",
       colour = "Method",
       y = "Bias of Network Estimation")

plot_bias

5 Centrality

5.1 Plot most central identical

plot_mostcentral <- sr_edit |> 
  # if mcse is missing, set to 0
  mutate(mcse = ifelse(is.na(mcse), 0, mcse)) |>
  mutate(outcome = factor(outcome, levels = c("Temporal", "Contemporaneous"))) |>
  filter(pm == "mostcent") |> 
  mutate(n_tp = paste0("t = ", n_tp)) |>
  mutate(n_tp = factor(n_tp, levels = c("t = 60", "t = 120"))) |>
  mutate(n_id = paste0("n = ", n_id)) |>
  mutate(n_id = factor(n_id, levels = c("n = 75", "n = 200"))) |>
  ggplot(aes(x = as.factor(n_tp), 
             y = mean,
             group = method,
             colour = method
             )) +
  # horizontal line at chance level of 1/6
  geom_hline(yintercept = 1/6, 
             linetype = 2, 
             alpha = .7)+
  # add vertical line between methods
  geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
  geom_errorbar(aes(ymin = mean - 1*mcse,
                            ymax = mean + 1*mcse),
                        width = .5,
                 position = position_dodge(0.8),
                 show.legend = FALSE)+
  geom_point(position = position_dodge(0.8), 
             size = 1.4) +
  # add mean as text above errorbar
    geom_text(aes(label = sub("^(-?)0.", "\\1.",sprintf("%.2f", mean))),
              position = position_dodge(0.8),
              vjust = -1.0,
              size = 4,
              show.legend = FALSE) +
  ggh4x::facet_nested(n_id ~ outcome,
                      axes = "all",
                      remove_labels = "y") +
  # scale_x_discrete(guide = guide_axis(angle = 90))+
  scale_y_continuous(expand = c(0, 0), limits = c(0,1.1)) +
  scale_color_manual(values = meth_colors) +
  theme_centrality() +
  theme(legend.position = "bottom",
        text = element_text(size = 24),
        
        )+
  labs(title = "",
       x = "Time Points",
       colour = "",
       y = "Proportion of Correct Central Nodes")

ggsave("plot_mostcentral.pdf", plot_mostcentral, height = 6 * 1.1, width = 9 * 1.1,
       path = here::here("figures/"), device = "pdf")

plot_mostcentral

5.2 Plot rank correlation of centrality measures

We were interested in the performance of centrality estimation, which we assessed with regard to rank-order performance. As we expected centrality estimates to be biased downwards in some methods due to sparsity assumptions, we computed the rank-order consistency of individual centrality estimates. To do so, we computed the point estimate of network centrality \(\hat{c}\) per individual in a data set, which ignored estimation uncertainty. We then estimated the Spearman rank correlation \(\hat{\rho}_{i}\) in repetition \(i\) of these estimates with the true network centrality \(c\) and calculated its average across repetitions as: \[\begin{align*} \widehat{\rho} = \frac{\sum_{i=1}^{n_{\text{sim}}} \hat{\rho}_i}{n_{\text{sim}}} \end{align*}\] We calculated the MCSE of this correlation via bootstrapping.

plot_rankcor <- sr_edit |> 
  # if mcse is missing, set to 0
  mutate(mcse = ifelse(is.na(mcse), 0, mcse)) |>
  # uselessly used temp and cont instead of beta and pcor here
  mutate(outcome = case_when(
    outcome == "temp" ~ "Temporal",
    outcome == "cont" ~ "Contemporaneous"
  )) |>
  mutate(outcome = factor(outcome, levels = c("Temporal", "Contemporaneous"))) |>
  filter(pm == "rankcor") |> 
  ggplot(aes(x = method, 
             y = mean, 
             colour = method
             )) +
  # add vertical line between methods
  geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
  geom_errorbar(aes(ymin = mean - 1*mcse,
                            ymax = mean + 1*mcse),
                        width = .8,
                 position = position_dodge(0.7),
                 show.legend = FALSE)+
  geom_point(position = position_dodge(0.7), 
             size = 1.2) +
  ggh4x::facet_nested(n_id ~ outcome + n_tp,
                      axes = "all",
                      remove_labels = "y") +
  scale_x_discrete(guide = guide_axis(angle = 90))+
  scale_y_continuous(expand = c(0, 0), limits = c(0,1.1)) +
  scale_color_manual(values = meth_colors) +
  theme_centrality() +
  theme(legend.position = "none",
        text = element_text(size = 22))+
  labs(title = "",
       x = "Method",
       colour = "Method",
       y = "Centrality Rank Correlation")


ggsave("plot_rankcor.pdf", plot_rankcor, height = 12, width = 16,
       path = here::here("figures/"), device = "pdf")

plot_rankcor

6 Regression

6.1 Power of Regression

6.1.1 In- and Outstrength combined

Prep data

# Split data set into three based on true effect
power_df <- sr_edit |> 
  filter(!str_detect(pm, "poweroneside")) |> 
  mutate(pm = str_replace(pm, "powertwoside", "power")) |> 
  filter(str_detect(pm, "power")) |> 
  mutate(outcome = case_when(
    # outcome == "tempdens" ~ "Temporal\nDensity",
    # outcome == "contdens" ~ "Contemporaneous\nDensity",
    outcome == "outstrength" ~ "Temporal\nOutstrength",
    outcome == "strength" ~ "Contemporaneous\nStrength",
    outcome == "instrength" ~ "Temporal\nInstrength"
  )) |>
  # For now, remove contemporaneous strength
  filter(outcome != "Contemporaneous\nStrength") |>
  mutate(n_id = paste0("n = ", n_id)) |>
  mutate(n_id = factor(n_id, levels = c("n = 75", "n = 200"))) |>
  mutate(n_tp = paste0("t = ", n_tp)) |>
  mutate(n_tp = factor(n_tp, levels = c("t = 60", "t = 120"))) |>
  # split pm into two columns, take last number into new column
  separate_wider_delim(pm, delim = "reg", names = c("pm", "true_effect"))

power_list <- split(power_df, power_df$true_effect)

Function to create the plots:

# Function to create the plot for a given dataframe
power_plot <- function(df) {
  ggplot(df, aes(x = n_tp, 
                 y = mean, 
                 colour = method,
                 fill = method,
                 group = method)) +
    geom_errorbar(aes(ymin = mean - 1 * mcse,
                      ymax = mean + 1 * mcse),
                  width = 0.5,
                  position = position_dodge(0.7),
                  show.legend = FALSE) +
    # add vertical
    geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
    geom_point(position = position_dodge(0.7), 
               size = 1.4) +
    ggh4x::facet_nested(n_id ~ outcome,
                        axes = "all",
                        remove_labels = "y") +
    # scale_x_discrete(guide = guide_axis(angle = 90)) +
    scale_y_continuous(expand = c(0, 0), limits = c(-0.1, 1.1)) +
    scale_color_manual(values = meth_colors) +
    theme_centrality() +
    theme(legend.position = "none",
          strip.text.x.top = ggplot2::element_text(size = rel(0.85)),
          ggh4x.facet.nestline = element_line(colour = "#6d6d6e"),
          axis.text = element_text(size = 18)) +
    labs(title = "",
         x = "",
         colour = "",
         fill = "",
         group = "",
         y = "Detection Rate")
}

Create the plots and combine them with patchwork

plot_power_list <- lapply(power_list, power_plot)

# add legend to the third plot
plot_3_legend <- plot_power_list[[3]] + 
  theme(legend.position = "bottom",
        text = element_text(size = 25))

# extract legend
legend <- cowplot::get_plot_component(plot_3_legend, 'guide-box-bottom', return_all = TRUE)

# add legend to cowplot

plot_power_combined <- cowplot::plot_grid(plot_power_list[[1]],
                                          plot_power_list[[2]],
                                          plot_power_list[[3]],
                                          legend,
                                          ncol = 1,
                                          nrow = 4,
                                          rel_heights = c(1, 1, 1, 0.1),
                                          labels = c("True Effect: 0", 
                                                     "True Effect: 0.2",
                                                     "True Effect: 0.4",
                                                     ""),
                                          label_fontfamily = "news",
                                          label_size = 18)




ggsave("plot_power_combined.pdf", plot_power_combined, height = 16* 0.95, width = 16* 0.8,
       path = here::here("figures/"))
ggsave("plot_power_combined.svg", plot_power_combined, height = 16* 0.95, width = 16* 0.8,
       path = here::here("scripts", "simulation_viz_figures"))

How large was the difference between instrength and outstrength?

power_df |> 
  pivot_wider(id_cols = c(dgp, n_id, n_tp, pm, true_effect, method), 
              names_from = outcome, 
              values_from = c(mean, mcse)) |> 
  filter(true_effect != 0) |> 
  janitor::clean_names() |> 
  mutate(mean_diff = mean_temporal_instrength - mean_temporal_outstrength) |> 
  summarize(mean_mean_diff = mean(mean_diff)) |> 
  knitr::kable()

mean_mean_diff
0.0521875

6.2 Power and Bias for Outstrength

This reproduces the simulation figure in the manuscript.

power_bias_reg_combined_df <- sr_edit |> 
  mutate(pm = str_replace(pm, "powertwoside", "power")) |> 
  filter(!str_detect(pm, "poweroneside")) |>
  filter(str_detect(pm, "power") | str_detect(pm, "biasreg")) |> 
    mutate(outcome = case_when(
    outcome == "outstrength" ~ "Temporal\nOutstrength",
    outcome == "strength" ~ "Contemporaneous\nStrength",
    outcome == "instrength" ~ "Temporal\nInstrength"
  )) |>
  filter(outcome == "Temporal\nOutstrength") |> 
  mutate(n_id = paste0("n = ", n_id)) |>
  mutate(n_id = factor(n_id, levels = c("n = 75", "n = 200"))) |>
  mutate(n_tp = paste0("t = ", n_tp)) |>
  mutate(n_tp = factor(n_tp, levels = c("t = 60", "t = 120"))) |>
  # split pm into two columns, take last number into new column
  separate_wider_delim(pm, delim = "reg", names = c("pm", "true_effect")) |> 
  mutate(method = factor(method, levels = c("GVAR", "GIMME", "mlVAR", "BmlVAR"))) |> 
  mutate(true_effect = paste0("True Effect: .", true_effect)) |> 
  mutate(pm = case_when(
    str_detect(pm, "power") ~ "Detection Rate",
    str_detect(pm, "bias") ~ "Bias"
  ))

plot_power_bias_outstrength <- power_bias_reg_combined_df |>
  ggplot(aes(x = n_tp, 
             y = mean, 
             colour = method,
             fill = method,
             group = method))+
  geom_errorbar(aes(ymin = mean - 1 * mcse,
                      ymax = mean + 1 * mcse),
                  width = 0.5,
                  position = position_dodge(0.8),
                  show.legend = FALSE) +
    # add vertical
    geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
    geom_point(position = position_dodge(0.8), 
               size = 1.4) +
    # add mean without leading zero
    geom_text(aes(label = sub("^(-?)0.", "\\1.",sprintf("%.2f", mean))),
              position = position_dodge(0.8),
              vjust = -0.6,
              size = 5,
              show.legend = FALSE) +
    ggh4x::facet_nested(true_effect + n_id ~ pm,
                        axes = "all",
                        scales = "free_y",
                        independent = "y") +
    facetted_pos_scales(
      y = list(pm == "Bias" ~ scale_y_continuous(expand = c(0, 0), limits = c(-.45, .2)),
               pm == "Detection Rate" ~ scale_y_continuous(expand = c(0, 0), limits = c(-0.1, 1.1)))
    )+
    labs(
      title = "",
      x = "Time Points",
      colour = "",
      fill = "",
      group = "",
      y = ""
    ) +
    scale_color_manual(values = meth_colors) +
    theme_centrality() +
    theme(legend.position = "bottom",
          ggh4x.facet.nestline = element_line(colour = "#6d6d6e"),
          axis.text.x = element_text(size = 22),
          axis.text.y = element_text(size = 22),
          axis.title.x = element_text(size = 24),
          # increase all legend element size
          legend.text = element_text(size = 24),
          legend.title = element_text(size = 24),
          legend.key.size = unit(1.6, "lines"),
          strip.text = ggplot2::element_text(size = 24),
          strip.text.x.top = ggplot2::element_text(size = 24)
          )

ggsave("plot_power_bias_outstrength.pdf", 
       plot_power_bias_outstrength, height = 16* 0.95, width = 16* 0.8,
       path = here::here("figures/"))

6.3 Power and Bias for Contemporaneous Strength

power_bias_reg_strength_df <- sr_edit |> 
  mutate(pm = str_replace(pm, "powertwoside", "power")) |> 
  filter(!str_detect(pm, "poweroneside")) |>
  filter(str_detect(pm, "power") | str_detect(pm, "biasreg")) |> 
    mutate(outcome = case_when(
    outcome == "outstrength" ~ "Temporal\nOutstrength",
    outcome == "strength" ~ "Contemporaneous\nStrength",
    outcome == "instrength" ~ "Temporal\nInstrength"
  )) |>
  filter(outcome == "Contemporaneous\nStrength") |> 
  mutate(n_id = paste0("n = ", n_id)) |>
  mutate(n_id = factor(n_id, levels = c("n = 75", "n = 200"))) |>
  mutate(n_tp = paste0("t = ", n_tp)) |>
  mutate(n_tp = factor(n_tp, levels = c("t = 60", "t = 120"))) |>
  # split pm into two columns, take last number into new column
  separate_wider_delim(pm, delim = "reg", names = c("pm", "true_effect")) |> 
  mutate(method = factor(method, levels = c("GVAR", "mlVAR", "GIMME", "BmlVAR"))) |> 
  mutate(true_effect = paste0("True Effect: .", true_effect)) |> 
  mutate(pm = case_when(
    str_detect(pm, "power") ~ "Detection Rate",
    str_detect(pm, "bias") ~ "Bias"
  ))

plot_power_bias_strength <- power_bias_reg_strength_df |>
  ggplot(aes(x = n_tp, 
             y = mean, 
             colour = method,
             fill = method,
             group = method))+
  geom_errorbar(aes(ymin = mean - 1 * mcse,
                      ymax = mean + 1 * mcse),
                  width = 0.5,
                  position = position_dodge(0.8),
                  show.legend = FALSE) +
    # add vertical
    geom_vline(colour = "#F3F4F5", xintercept = seq(1.5, 4, 1))+
    geom_point(position = position_dodge(0.8), 
               size = 1.4) +
    # add mean as text above errorbar
    geom_text(aes(label = round(mean, 2)),
              position = position_dodge(0.8),
              vjust = -0.6,
              size = 5,
              show.legend = FALSE) +
    ggh4x::facet_nested(true_effect + n_id ~ pm,
                        axes = "all",
                        scales = "free_y",
                        independent = "y") +
    facetted_pos_scales(
      y = list(pm == "Bias" ~ scale_y_continuous(expand = c(0, 0), limits = c(-.45, .2)),
               pm == "Detection Rate" ~ scale_y_continuous(expand = c(0, 0), limits = c(-0.1, 1.1)))
    )+
    labs(
      title = "",
      x = "Timepoints",
      colour = "",
      fill = "",
      group = "",
      y = ""
    ) +
    scale_color_manual(values = meth_colors) +
    theme_centrality() +
    theme(legend.position = "bottom",
          ggh4x.facet.nestline = element_line(colour = "#6d6d6e"),
          axis.text = element_text(size = 18),
          # increase all legend element size
          legend.text = element_text(size = 18),
          legend.title = element_text(size = 18),
          legend.key.size = unit(1.5, "lines"),
          strip.text = ggplot2::element_text(size = 24),
          strip.text.x.top = ggplot2::element_text(size = 24)
          )

ggsave("plot_power_bias_strength.pdf", 
       plot_power_bias_strength, height = 16* 0.95, width = 16* 0.8,
       path = here::here("figures/"))
ggsave("plot_power_bias_strength.svg", 
       plot_power_bias_strength, height = 16* 0.95, width = 16* 0.8,
       path = here::here("scripts", "simulation_viz_figures"), device = "svg")

6.4 RMSE and Bias of Regression

We create plot for different regression outcomes here:

process_data <- function(data, summary) {
  df_clean <- data |> 
    filter(str_detect(pm, summary)) |> 
    mutate(outcome = case_when(
      outcome == "outstrength" ~ "Temporal\nOutstrength",
      outcome == "strength" ~ "Contemporaneous\nStrength",
      outcome == "instrength" ~ "Temporal\nInstrength"
    )) |>
    filter(outcome != "Contemporaneous\nStrength") |> 
    mutate(
      n_id = factor(paste0("n = ", n_id), levels = c("n = 75", "n = 200")),
      n_tp = factor(paste0("t = ", n_tp), levels = c("t = 60", "t = 120"))
    ) |>
    separate_wider_delim(pm, delim = "reg", names = c("pm", "true_effect"))
  
    split(df_clean, df_clean$true_effect)
}

## Generic plotting function
create_regression_plot <- function(df, 
                                   y_label) {
  ggplot(data = df,
         aes(
           x = n_tp,
           y = mean,
           colour = method,
           fill = method,
           group = method
         )) +
    # add horizontal dashed line at zero for bias
    geom_hline(yintercept = 0, linetype = 2, alpha = .4)+
    geom_errorbar(
      aes(ymin = mean - 1 * mcse, ymax = mean + 1 * mcse),
      width = .5,
      position = position_dodge(0.7),
      show.legend = FALSE
    ) +
    geom_point(position = position_dodge(0.7), size = 1.2) +
    ggh4x::facet_nested(n_id ~ outcome,
                        axes = "all",
                        remove_labels = "y") +
    scale_y_continuous(expand = c(0, 0), limits = c(-.45, .2)) +
    scale_color_manual(values = meth_colors) +
    theme_centrality() +
    theme(
      legend.position = "none",
      strip.text.x.top = ggplot2::element_text(size = rel(0.85)),
      ggh4x.facet.nestline = element_line(colour = "#6d6d6e"),
      axis.text = element_text(size = 18)
    ) +
    labs(
      title = "",
      x = "",
      colour = "",
      group = "",
      fill = "",
      y = y_label
    )
}

## Generate and save combined plots
generate_regression_plots <- function(data, summary, y_label, file_name) {
  processed_list <- process_data(data, summary)
  plot_list <- lapply(processed_list, create_regression_plot, y_label = y_label)
  combined_plot <- cowplot::plot_grid(
    plotlist = plot_list, 
    ncol = 1,
    labels = c("True Effect: 0", "True Effect: 0.2", "True Effect: 0.4")
  )
  ggsave(file_name, combined_plot, height = 16 * 0.95, width = 16 * 0.8, 
         path = here::here("figures/"))
}


## RMSE Plot
generate_regression_plots(sr_edit, "rmsereg", "RMSE", "plot_reg_rmse_combined.pdf")

## Bias Plot
generate_regression_plots(sr_edit, "biasreg", "bias", "plot_reg_bias_combined.pdf")

7 MCMC Diagnostics

We can now look at the Bayesian models in more detail and check if the Rhats are satisfactory, as well as if there were any divergent transitions.

First, look at Rhats:

sim_results |> 
  select(bmlvar_diagnostics.rhat_bmlvar_mean) |> 
  rename("Mean Rhat" = bmlvar_diagnostics.rhat_bmlvar_mean) |> 
  knitr::kable()

Mean Rhat
1.0002140
0.9996671
1.0001584
0.9998736

Second, we tabulate divergent transitions:

sim_results |> 
  select(contains("divtrans")) |> 
  rename_with(~ str_remove(., "bmlvar_diagnostics."), everything()) |> 
  knitr::kable(col.names = c("Mean Number of DivTrans",
                            "Sum of DivTrans",
                            "Models with Divtrans"))

Mean Number of DivTrans	Sum of DivTrans	Models with Divtrans
4.390	878	100
0.005	1	1
1.310	262	26
0.000	0	0

8 Session Info

pander::pander(sessionInfo())

R version 4.4.2 (2024-10-31)

Platform: x86_64-pc-linux-gnu

locale: LC_CTYPE=en_US.UTF-8, LC_NUMERIC=C, LC_TIME=en_US.UTF-8, LC_COLLATE=en_US.UTF-8, LC_MONETARY=en_US.UTF-8, LC_MESSAGES=en_US.UTF-8, LC_PAPER=en_US.UTF-8, LC_NAME=C, LC_ADDRESS=C, LC_TELEPHONE=C, LC_MEASUREMENT=en_US.UTF-8 and LC_IDENTIFICATION=C

attached base packages: stats, graphics, grDevices, utils, datasets, methods and base

other attached packages: MetBrewer(v.0.2.0), pander(v.0.6.5), ggh4x(v.0.2.8), cowplot(v.1.1.3), here(v.1.0.1), SimDesign(v.2.18), lubridate(v.1.9.4), forcats(v.1.0.0), stringr(v.1.5.1), dplyr(v.1.1.4), purrr(v.1.0.2), readr(v.2.1.5), tidyr(v.1.3.1), tibble(v.3.2.1), ggplot2(v.3.5.1) and tidyverse(v.2.0.0)

loaded via a namespace (and not attached): gtable(v.0.3.6), xfun(v.0.50), htmlwidgets(v.1.6.4), tzdb(v.0.4.0), vctrs(v.0.6.5), tools(v.4.4.2), generics(v.0.1.3), curl(v.6.2.0), parallel(v.4.4.2), pkgconfig(v.2.0.3), R.oo(v.1.27.0), RPushbullet(v.0.3.4), lifecycle(v.1.0.4), farver(v.2.1.2), compiler(v.4.4.2), textshaping(v.1.0.0), brio(v.1.1.5), munsell(v.0.5.1), janitor(v.2.2.1), codetools(v.0.2-20), snakecase(v.0.11.1), htmltools(v.0.5.8.1), snow(v.0.4-4), yaml(v.2.3.10), pillar(v.1.10.1), R.utils(v.2.12.3), sessioninfo(v.1.2.2), parallelly(v.1.41.0), tidyselect(v.1.2.1), digest(v.0.6.37), stringi(v.1.8.4), future(v.1.34.0), showtextdb(v.3.0), listenv(v.0.9.1), labeling(v.0.4.3), rprojroot(v.2.0.4), fastmap(v.1.2.0), grid(v.4.4.2), colorspace(v.2.1-1), cli(v.3.6.3), beepr(v.2.0), magrittr(v.2.0.3), future.apply(v.1.11.3), withr(v.3.0.2), scales(v.1.3.0), showtext(v.0.9-7), timechange(v.0.3.0), rmarkdown(v.2.29), sysfonts(v.0.8.9), globals(v.0.16.3), audio(v.0.1-11), progressr(v.0.15.1), ragg(v.1.3.3), ggokabeito(v.0.1.0), R.methodsS3(v.1.8.2), hms(v.1.1.3), pbapply(v.1.7-2), evaluate(v.1.0.3), knitr(v.1.49), testthat(v.3.2.3), rlang(v.1.1.5), Rcpp(v.1.0.14), glue(v.1.8.0), svglite(v.2.1.3), rstudioapi(v.0.17.1), jsonlite(v.1.8.9), R6(v.2.5.1) and systemfonts(v.1.2.1)